Label points in a plot

Here is my code:

h[θ_] := (1 - θ)/θ
x = Plot[{h[θ], 2.5}, {θ, 0.1, 1},
PlotTheme -> "Monochrome",
AxesLabel -> {"θ", "h(θ)"},
PlotLegends -> Placed[{"h(θ)", "\!$$\*OverscriptBox[\(θ$$, $$^$$]\)"}, Below],
LabelStyle -> {FontSize -> 10},
Epilog -> {PointSize[0.01], Black, Point[{{0.2, 4}, {0.25, 3}, {0.4, 1.5}, {0.5, 1}}]}]


I want to label these 4 points as A,B,C,D, respectively. I tried to implement the answer from here, but I got lost with Map, Transpose, etc.

So, I would appreciate any help

2 Answers

No Map, no Transpose, no etc.

h[θ_]:=(1-θ)/θ;
x=Plot[{h[θ],2.5},{θ,0.1,1},
Epilog->{
Point[{0.2,4}],Text["A",{0.2,4},{-1,-1}],
Point[{0.25,3}],Text["B",{0.25,3},{-1,-1}],
Point[{0.4,1.5}],Text["C",{0.4,1.5},{-1,-1}],
Point[{0.5,1}],Text["D",{0.5,1},{-1,-1}]
}]


There. See how much easier that is to understand.

With Callouts and combining a separate ListPlot using a Show:

h[θ_] := (1 - θ)/θ
Show[
Plot[{h[θ], 2.5}, {θ, 0.1, 1},
PlotTheme -> "Monochrome", AxesLabel -> {"θ", "h(θ)"},
PlotLegends -> Placed[{"h(θ)", "\!$$\*OverscriptBox[\(θ$$, $$^$$]\)"}, Below],
LabelStyle -> {FontSize -> 10}],
With[{pts = {{0.2, 4}, {0.25, 3}, {0.4, 1.5}, {0.5, 1}}, labels = {"A","B","C","D"}},
ListPlot[Thread[Callout[pts, labels]]]
]
]